Air vehicle flight mechanism and control method

ABSTRACT

Heavier-than-air, aircraft having flapping wings, e.g., ornithopters, where angular orientation control is effected by variable differential sweep angles of deflection of the flappable wings in the course of sweep angles of travel and/or the control of variable wing membrane tension.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/US2010/037540 filed Jun. 4, 2010, which claims priority to andbenefit of U.S. Provisional Patent Application No. 61/184,748, filedJun. 5, 2009, which are hereby incorporated herein by reference in theirentirety for all purposes.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under contract no.W31P4Q-06-C-0435 awarded by the US Army Aviation and Missile Command.The US Government has certain rights in the invention.

TECHNICAL FIELD

Heavier-than-air, aircraft having flapping wings where angularorientation control is effected by variable differential sweep angles ofdeflection of the flappable wings in the course of sweep angles oftravel and/or the control of variable wing membrane tension.

BACKGROUND

Radio-controlled, heavier-than-air, aircraft having sustainable beatingwings, e.g., ornithopters.

SUMMARY

Exemplary embodiments of an air vehicle comprise a support structure,e.g., a structural element of a fuselage, where the support structuremay further comprise a flapping drive element, e.g., one or more motorsconfigured to generate flapping angular velocity, a first airfoilrotatably attached, e.g., via a joint, to the support structure and asecond airfoil rotatably attached, e.g., via a joint, to the supportstructure. The first airfoil may comprise a root-to-wingtip spar, ormast, a root spar, or boom, and a scrim, or membrane, attached to, e.g.,wrapped about or wrapped about a tube that is disposed about, the firstmast and the first root spar. The first airfoil is configured to bedriven to flap via the flapping drive element, e.g., via gearing,pulleys, and/or linkages. The second air foil comprises a second mast,second root spar, and a second membrane attached to the second root sparand the second mast. The second airfoil is also configured to be drivento flap via the flapping drive element. Air vehicle control about atleast one axis of the vehicle, e.g., pitch, yaw, or roll, is effected byat least one of: (a) variable membrane luffing, e.g., via increasing anddecreasing the angle between the mast and the root spar by the rotatingthe root spar relative to the mast thereby loosening or making taut thesurface of the membrane; (b) variable root spar rotation travellimitation, e.g., via repositionable boom tip travel stops, and (c)variable motor drive speed, e.g., via a flapping drive elementcomprising two motors, each driving one airfoil.

Exemplary embodiments include an air vehicle control device comprising:a first flappable wing having a sweep angle of travel, wherein the firstflappable wing comprises a membrane attached to a root spar and a mast,the membrane having surface tension adjustable via rotation of the rootspar relative to the mast; a second flappable wing having a sweep angleof travel, wherein the second flappable wing comprises a second membraneattached to a second root spar and a second mast, the membrane havingsurface tension adjustable via rotation of the second root spar relativeto the second mast; wherein the first flappable wing extends in a radialdirection from the air vehicle and the second flappable wing extends ina radial direction from a side of the air vehicle substantially oppositethe first flappable wing; and thereby configured to generate at leastone of: a pitching torque, a rolling torque and a yawing torque, bygenerating a difference between luffing of the first flappable wing andluffing of the second flappable wing. Other exemplary embodiments havethe first flappable wing further comprising a sweep angle of deflectioncomprising a forward sweep angle of deflection and a backward sweepangle of deflection; and a second flappable wing further comprising asweep angle of deflection comprising a forward sweep angle of deflectionand a backward sweep angle of deflection; where the device is furtherconfigured to generate a yawing torque, by generating at least one of: adifference between the forward sweep angle of deflection of the firstflappable wing and the forward sweep angle of deflection of the secondflappable wing, and a difference between the backward sweep angle ofdeflection of the first flappable wing and the backward sweep angle ofdeflection of the second flappable wing.

Exemplary embodiments include an assembly comprising: (a) a first armrotatably attached to a support structure and a second arm rotatablyattached to the support structure; (b) a first wing comprising amembrane attached to a first mast and a first root spar, the first wingmast rotationally attached to a first arm, and the first root sparattached to a luffing control assembly; and (c) a second wing comprisinga membrane attached to a second mast and a second root spar, the secondwing mast rotationally attached to a second arm, and the second rootspar attached to the luffing control assembly. The luffing controlassembly may comprise a first yang attached to the first root spar whileallowing for some rotational travel of the first root spar about themast longitudinal axis, a second yang attached to the second root sparwhile allowing for some rotational travel of the second root spar aboutthe mast longitudinal axis, and a repositionable yang yoke configured toreceive the first yang and the second yang. Other exemplary embodimentsinclude the first arm further comprising a first repositionable stop anda second repositionable stop together defining a rotation angle of thefirst wing root spar about the first wing mast; and the second armfurther comprising a third repositionable stop and a fourthrepositionable stop together defining a rotation angle of the secondwing rootspar about the second wing mast.

Embodiments also include a method of air vehicle control comprising (inno particular order): (a) providing: (i) a first flappable wing having asweep angle of travel, and having a sweep angle of deflection comprisinga forward sweep angle of deflection and a backward sweep angle ofdeflection; and (ii) a second flappable wing having a sweep angle oftravel, and having a sweep angle of deflection comprising a forwardsweep angle of deflection and a backward sweep angle of deflection;wherein the first flappable wing extends in a radial direction from theair vehicle and the second flappable wing extends in a radial directionfrom a side of the air vehicle substantially opposite the firstflappable wing; and (b) generating at least one of: a rolling torque anda yawing torque, by generating at least one of: a difference between theforward sweep angle of deflection of the first flappable wing and theforward sweep angle of deflection of the second flappable wing, and adifference between the backward sweep angle of deflection of the firstflappable wing and the backward sweep angle of deflection of the secondflappable wing. The method of air vehicle control may further comprisegenerating a pitching torque by changing the forward angle of deflectionof the first flappable wing based on its sweep angle and by changing theforward angle of deflection of the second flappable wing based on itssweep angle. Some embodiments of the invention may further comprisegenerating a pitching torque by changing the backward angle ofdeflection of the first flappable wing based on its sweep angle and bychanging the backward angle of deflection of the second flappable wingbased on its sweep angle.

Embodiments may also include a flapping device comprising: (a) arotating element having a center of rotation and a plane of rotation;(b) a first capstan mounted about a shaft, the shaft attached to therotating element distal from the center of rotation and substantiallyperpendicular to the plane of rotation; (c) a first rocker memberrotatably attached to a support structure; (d) a first drive linkrotatably attached to the first capstan and the first rocker member; (e)a first arm rotatably attached to the support structure and rotatablyattached to the first rocker member via a first rocker link; (f) asecond capstan mounted about the shaft; (g) a second rocker memberrotatably attached to the support structure; (h) a second drive linkrotatably attached to the second capstan and the second rocker member;and (i) a second arm rotatably attached to the support structure androtatably attached to the second rocker member via a second rocker link.Some embodiments of the mechanism embodiment have the rotating elementrotatably attached to the support structure.

Embodiments may also include an assembly comprising: (a) a first armrotatably attached to a support structure and a second arm rotatablyattached to the support structure; (b) a first wing comprising a firstmast and a first spar, the first wing mast rotationally attached to afirst arm, the first arm having a first repositionable stop and a secondrepositionable stop together defining a rotation angle of the first wingspar about the first wing mast; and (c) a second wing comprising asecond mast and a second spar, the second wing mast rotationallyattached to a second arm, the second arm having a third repositionablestop and a fourth repositionable stop together defining a rotation angleof the second wing spar about the second wing mast. Some embodiments ofthe assembly have the first stop disposed on a first pulley and thesecond stop disposed on a second pulley, where the first pulley and thesecond pulley are each rotatably repositionable via an actuated linkingmember and where the third stop and fourth stop are each rotatablyrepositionable via a second actuated linking member.

Some embodiments of the assembly have the first stop disposed on a firstpulley and the second stop disposed on a second pulley, where the firstpulley and the second pulley are each rotatably repositionable via anactuated linking member to increase a first angle subtended by the firststop and the second stop, and the third stop and fourth stop are eachrotatably repositionable via a second actuated linking member toincrease a second angle subtended by the third stop and the fourth stop.

Embodiments may also include a mechanism comprising: (a) a rotatingelement having a center of rotation and a plane of rotation; (b) a firstcapstan mounted about a shaft, the shaft attached to the rotatingelement distal from the center of rotation and substantiallyperpendicular to the plane of rotation; (c) a second capstan mountedabout the shaft; (d) a first arm mounted to a third capstan, a firstlinking member connecting the third capstan with the first capstan; (e)a second arm mounted to a fourth capstan, a second linking memberconnecting the fourth capstan with the second capstan; and (f) a thirdlinking member connecting the third capstan with the fourth capstan. Insome embodiments of the mechanism, the third capstan of the mechanismmay have a center of rotation, the fourth capstan may have a center ofrotation, and the center of rotation of the rotating element may besubstantially collinear with both the center of rotation of the thirdcapstan and the center of rotation of the fourth capstan. In someembodiments of the mechanism, the first linking member may comprise acord, the second linking member may comprise a cord, and the thirdlinking member may comprise a cord.

Embodiments may also include a wing comprising: (a) a mast engaging afitment; (b) a spar engaging a fitment substantially perpendicular tothe mast; (c) a mast tube disposed about a portion of the mast; (d) aspar tube disposed about a portion of the spar; (e) a scrim attached tothe spar tube and the mast tube; and (f) a first batten disposed on thescrim and extending in a direction radially from the intersection of thespar and the mast, the first batten having a distal end proximate to anedge of the airfoil. Some embodiments of the wing further comprise astrut disposed proximate to the intersection of the mast and the spar,the strut attached to the mast and the spar. Some embodiments of thewing have the first batten further comprising a proximal end attached tothe strut. Some embodiments of the wing may further comprise a secondbatten disposed on the scrim and extending in a direction radially fromthe intersection of the spar and the mast, the second batten having adistal end proximate to an edge of the airfoil. Some embodiments of thewing have the second batten further comprising a proximal end attachedto the strut. Still other embodiments of the wing further comprise aroot socket configured to fixedly receive the spar and configured torotatably receive the mast. In some embodiments, the planform of thewing is defined by perimeter points comprising: the distal end of thefirst batten, a distal end portion of the mast, a distal end portion ofthe spar, a proximal end portion of the mast, and a proximal end portionof the spar. In some embodiments, the planform of the wing is defined byperimeter points comprising: the distal end of the first batten, thedistal end of the second batten, a distal end portion of the mast, adistal end portion of the spar, a proximal end portion of the mast, anda proximal end portion of the spar. Some embodiments of the wing have ascrim comprising a polyvinyl fluoride film and some other embodiments ofthe wing have a scrim comprising a polyvinyl fluoride film furthercomprising a fiber mesh. For some embodiments of the wing, the scrimcomprises a fiber mesh comprising intersecting lines of fiber mesh, thelines of fiber mesh may be oriented at oblique angles relative to thespar tube and relative to the mast tube. Some embodiments of the winghave the mast comprising a carbon rod and the first batten may comprisea carbon rod.

A flapping drive element may comprise two or more motors, flap ratesensors, and circuitry to control and adjust the flap rates of the twoairfoils, each attached to an arm of the flapping drive element. Forexample, a flapping drive element may comprise a first motor driving afirst rotating element, the first rotating element having a center ofrotation and a plane of rotation; a first capstan mounted about a shaft,the shaft attached to the rotating element distal from the center ofrotation and substantially perpendicular to the plane of rotation; asecond capstan mounted about the shaft; a first arm mounted to a thirdcapstan, a first linking member connecting the third capstan with thefirst capstan; a second linking member connecting the fourth capstanwith the second capstan; and a third linking member connecting the thirdcapstan with the fourth capstan; a second motor driving a secondrotating element, the second rotating element having a center ofrotation and a plane of rotation; a fifth capstan mounted about a secondshaft, the second shaft attached to the second rotating element distalfrom the center of rotation and substantially perpendicular to the planeof rotation of the second rotating element; a sixth capstan mountedabout the second shaft; a fourth linking member connecting the seventhcapstan with the fifth capstan; a second arm mounted to a eighthcapstan, a fifth linking member connecting the eighth capstan with thesixth capstan; and a sixth linking member connecting the seventh capstanwith the eighth capstan; and circuitry controlling a flapping rate ofthe first motor and the second motor.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention are illustrated by way of example and notlimitation in the figures of the accompanying drawings, and in which:

FIG. 1 depicts an aircraft having two flapping airfoils;

FIG. 2A depicts an exemplary airfoil;

FIG. 2B depicts the flexibility and luffing of the exemplary airfoil ofFIG. 2A;

FIG. 2C depicts the flexibility and luffing of the exemplary airfoil ofFIG. 2A; FIG. 3A depicts in a top view an aircraft having a nose tiporiented in the forward direction with its left airfoil deflected lessthan its right airfoil in a forward stroke of the wings;

FIG. 3B depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected less than itsright airfoil in a backward stroke of the wings;

FIG. 3C depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected more than itsright airfoil in a forward stroke of the wings;

FIG. 3D depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected less than itsright airfoil in a backward stroke of the wings;

FIG. 4A depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 3Aand 3B;

FIG. 4B depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 3Aand 3B;

FIG. 4C depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 3Cand 3D;

FIG. 4D depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 3Cand 3D;

FIG. 5A depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected less than itsright airfoil in a backward stroke of the wings;

FIG. 5B depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected more than itsright airfoil in a forward stroke of the wings;

FIG. 5C depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected more than itsright airfoil in a backward stroke of the wings;

FIG. 5D depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil deflected less than itsright airfoil in a forward stroke of the wings;

FIG. 6A depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 5Aand 5B;

FIG. 6B depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 5Cand 5D;

FIG. 7A depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil and its right airfoil bothdeflected less in the beginning of a forward stroke (fore stroke) of thewings than the deflection at the end of the forward stroke which isdepicted as larger in deflected angle;

FIG. 7B depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil and its right airfoil bothdeflected more in the beginning of a backward stroke (backstroke) of thewings than the deflection at the end of the backward stroke which isdepicted as smaller in deflected angle;

FIG. 7C depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil and its right airfoil bothdeflected more in the beginning of a forward stroke (fore stroke) of thewings than the deflection at the end of the forward stroke which isdepicted as smaller in deflected angle;

FIG. 7D depicts in a top view an aircraft having a nose tip oriented inthe forward direction with its left airfoil and its right airfoil bothdeflected less in the beginning of a backward stroke (backstroke) of thewings than the deflection at the end of the backward stroke which isdepicted as larger in deflected angle;

FIG. 8A depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 7Aand 7B;

FIG. 8B depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 7Aand 7B;

FIG. 8C depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 7Cand 7D;

FIG. 8D depicts instantaneous thrust vectors and cumulative thrustvectors for the left and right sides of a vehicle such as in FIGS. 7Cand 7D;

FIG. 9 depicts an exemplary flapping drive assembly including a motor, agearing assembly, a left arm and a right arm rotatably attached at a pinof a drive gear, where the pin is offset from the center of rotation ofthe drive gear;

FIG. 10A depicts a portion of the drive assembly of FIG. 10B;

FIG. 10B depicts an exemplary flapping drive assembly and mechanism;

FIG. 11A depicts in exploded view an exemplary wing;

FIG. 11B depicts an assembled exemplary wing;

FIG. 12 depicts an exemplary flapping drive assembly and mechanism,similar to combining a pair of the embodiments of FIG. 10, where eachhas four capstans;

FIG. 13 depicts an exemplary assembly for limiting root spar, or boom,travel;

FIGS. 14A-14C depict in a side view the exemplary assembly of FIG. 13;

FIG. 15A depicts the motion of a string to rotate the position of afirst boom stop by rotating a first pulley element about a pivot pointon a support structure;

FIG. 15B depicts in a bottom up view the boom stops extended of arelatively high deflecting angle of the boom for a first wing positionof a stroke;

FIG. 15C depicts in a bottom up view the boom stops extended of arelatively high deflecting angle of the boom for a second wing positionof a stroke;

FIG. 16 depicts a wing assembly and the pair of pulley elements for theboom stops;

FIG. 17A depicts an example where each boom stop is positioned to allowfor a relatively large deflection angle, compared to 17B, for both theforward stroke and the backward stroke;

FIG. 17B depicts an example where each boom stop is positioned to allowfor a relatively small deflection angle, compared to 17A, for both theforward stroke and the backward stroke;

FIG. 18A depicts stops in a neutral position as to the yaw channel;

FIG. 18B depicts stops biased to the right where the flapping of thewing and movement of the boom between the two stops—to one stop duringthe forward stroke and to the other stop during the rearwardstroke—would generate a thrust vector having a right-oriented component;

FIG. 18C depicts stops biased to the left where the flapping of the wingand movement of the boom between the two stops—to one stop during theforward stroke and to the other stop during the rearward stroke—wouldgenerate a thrust vector having a left-oriented component;

FIG. 19 depicts an alternate means of boom travel control where a cordor string is controlled by a servo and fed, via eyelets, to the boom andfixed at a distal portion of the boom;

FIG. 20A depicts control of the orientation of the boom during flappingmay be effected by rotating the cord or string to position the boom fora backward stoke;

FIG. 20B depicts control of the orientation of the boom during flappingmay be effected by rotating the cord or string to position the boom fora backward stoke;

FIG. 21A depicts a three-axis servo boom yang assembly;

FIG. 21B depicts an exemplary aircraft having a flapping mechanism;

FIG. 22 depicts a portion of an exemplary aircraft having a flappingmechanism;

FIG. 23 depicts a portion of an exemplary aircraft having a flappingmechanism;

FIG. 24A depicts the gimbaled yoke tilted toward the left airfoil andaway from the right airfoil;

FIG. 24B depicts the gimbaled yoke tilted toward the right airfoil andaway from the right airfoil;

FIG. 25A depicts a boom yang system where separate boom yang engages theyoke and provides structural support for a variable boom stop lever;

FIG. 25B-25D depict actuation of the boom stop lever for yaw control;

FIG. 26 is an exemplary top level block diagram of the control andpropulsion system of an aircraft embodiment;

FIG. 27 is a top level functional block diagram of a flapping frequencycontroller;

FIG. 28 is an exemplary top level block diagram of a servo controller;

FIG. 29 is an exemplary top level block diagram of an angular ratecontroller;

FIG. 30 is an exemplary top level block diagram of an angular ratecontroller;

FIG. 31 depicts an exemplary wing;

FIG. 32 depicts in cross sectional view the wing of FIG. 31;

FIG. 33 depicts in an edge on view of FIG. 31 depicting rotatability ofthe membrane about the mast;

FIG. 34 depicts in a cross section view of wing FIG. 31 the membranewrapped around a tube within which is disposed the mast, orroot-to-wingtip spar;

FIG. 35 depicts another means of attachment where a separate piece ofmaterial is used to attach the tube to the membrane;

FIG. 36 depicts another means of attachment where the membrane edge hasa t-shape portion when viewed edge on, and the t-shaped portion, ororthogonal edge surface, is inserted within the mast tube, and may beheld in place by the mast element;

FIG. 37 depicts an exemplary airfoil having two battens and membranefold-over portions;

FIG. 38 depicts an exemplary airfoil having two battens, membranefold-over portions, and where the battens have membrane overlays;

FIG. 39 depicts the airfoil of FIG. 37 where the membrane material is afoam membrane;

FIG. 40 depicts an airfoil without battens and no membrane fold-overs;

FIG. 41 depicts an airfoil having two battens, membrane fold-overs andan arcuate cutout region between the mast sleeve and the root sparsleeve;

FIG. 42 depicts an angular airfoil of relatively reduced surface area;

FIG. 43 depicts an airfoil made of a foam membrane having two curvingbattens, and membrane fold-overs;

FIG. 44 depicts a fixture for making an airfoil;

FIG. 45 depicts a membrane blank having a filament grid fixed to aworking surface;

FIG. 46 depicts the fixture of FIG. 44 positioned over the membraneblank;

FIG. 47 depicts a cut and fold-over step along the mast and root spar;

FIG. 50 depicts the battens applied to the surface of the membrane and acut step for the remainder of the planform; and

FIG. 51 depicts a removal of an exemplary airfoil from the blank.

DETAILED DESCRIPTION

Embodiments of the present invention include radio-controlled,heavier-than-air, aircraft having flapping wings, e.g., ornithopters,where the vehicle orientation control is effected by variabledifferential sweep angles of deflection of the flappable wings in thecourse of sweep angles of travel, variable differential luffing of thewings, and/or variable and differential angular velocity of wingflapping. Embodiments of the air vehicle comprise two wings, orairfoils, having the principal functions of providing lift andgenerating control moments or torques about the air vehicle. Either oftwo such airfoils may be disposed on each side of the fuselage, orstructural body, of the air vehicle. Each wing comprises aroot-to-wingtip spar, or mast, having a proximal end proximate to thewing root, and a distal end proximate to the wingtip. Each wingcomprises a root spar, or boom, proximate to the proximal end of themast, and the boom may be oriented, fixedly rotationally, but otherwisesubstantially orthogonal to the mast. A lifting surface membrane elementfor each wing is attached to the respective mast and the boom, and themembrane and boom may rotate or pivot about the longitudinal axis of themast. The wings may be driven by an onboard flapping drive element,e.g., at least one motor and mechanical movement so as to be flapped andtheir wingtips circumscribe arcs about the longitudinal axis of the airvehicle. If the boom is free to travel some angular amount about themast, then the distal end of the boom and the trailing edge of thelifting surface tend to trail the motion of the mast and leading portionof the lifting surface during flapping strokes. The distal end of theboom may be variably restrained relative to the mast, thereby variablylimiting the angular travel of the boom about the mast and/or varyingthe wing membrane slack, or luffing of the membrane. A thrust force maybe generated via the airfoils, each airfoil's thrust having aninstantaneous magnitude depending on the direction of mast flapping,i.e., a forward stroke or an backward stroke, the angle of each boomrelative to its respective mast and/or the amount of luffing in the wingmembrane and/or the angular velocity of the wing during the stroke.

FIG. 1 depicts an aircraft 100 having two airfoils 101, 102 a left(port) airfoil 101 and a right (starboard) airfoil 102, each attached tothe aircraft structure 103, such as the fuselage, and where the flappingin the forward direction of the aircraft, where the wingtips of theairfoils generally circumscribe arcs 104, 105 in the horizontal planeabout the aircraft 100 and, their respective extents of travel eachdefine a sweep angle of travel.

FIG. 2A depicts an exemplary airfoil 200 having a leading portion 201comprising a sleeve 202 for receiving a mast tube element and a sleeve203 for receiving a boom tube element. The airfoil as depicted includestwo stiffening elements, i.e., battens 204, 205, disposed on a surfacemembrane of the airfoil 200. FIG. 2B depicts the flexibility of theexemplary airfoil of FIG. 2A where the leading portion swings about apivot point 210, and in a plane orthogonal to the root spar sleeve 203,to circumscribe a flapping angle 211. FIG. 2C depicts the flexibility ofthe exemplary airfoil of FIG. 2B where the leading portion 201 isfurther swung about a pivot point and the distal end of the boomestablishes a sweep angle of deflection 220. The trailing edge 221 anddistal portion of the root spar, or boom, tends to trail the leadingportion 201, and if boom travel is permitted but limited, the distal endof the boom and the boom sleeve 203 will trail by a sweep angle ofdeflection 231. Generally, the larger the sweep angle of deflection, thelower the thrust generated by the airfoil. If the boom is permitted todecrease its angle relative to the mast 232, then the airfoil membranewill experience increased luffing. Generally, the greater the luffing,the lower the thrust generated by the airfoil.

FIG. 3A depicts in a top view an aircraft 310 having a nose tip 311oriented in the forward direction with its left airfoil 312 deflected,e.g., 20 degrees, an angle less than its right airfoil 313, e.g., 40degrees, in a forward stroke 314, 315 of each of the wings 312, 313.Accordingly, the left wing generates more thrust upward than the rightwing. FIG. 3B depicts in a top view the aircraft 310 having a nose tiporiented in the forward direction with its left airfoil 312 deflected,e.g., 20 degrees, an angle less than its right airfoil 313, e.g., 40degrees in a backward stroke 324, 325 of the wings 312, 313.Accordingly, this generates a roll moment about (over the top of) thevehicle 310. FIG. 3C depicts in a top view of the aircraft 310 having anose tip oriented in the forward direction with its left airfoil 312deflected, e.g., 40 degrees, and angle more than its right airfoil 313,e.g., 20 degrees in a forward stroke 314, 315 of the wings 312, 313.Accordingly, the right wing 313 generates more thrust upward than theleft wing 312. FIG. 3D depicts in a top view the aircraft 310 having anose tip oriented in the forward direction with its left airfoil 312deflected, e.g., 40 degrees, an angle more than its right airfoil 313,e.g., 20 degrees in a backward stroke 324, 325 of the wings 312, 313.Accordingly, this generates a roll moment about the vehicle 310 in theangular direction opposite that of FIG. 3B.

FIGS. 4A and 4B depict idealized instantaneous thrust vectors 410-413and idealized average cumulative thrust vectors 420-422 for the left andright sides of a vehicle, such as in FIGS. 3A and 3B. Exemplary wingdeflections are depicted for each wing at three positions in a stroke.Accordingly, the vehicle generates roll moment to effect a right roll,according to the right hand rule. FIGS. 4C and 4D depict idealizedinstantaneous thrust vectors 430-433 and idealized average cumulativethrust vectors 430-441 for the left and right sides of a vehicle such asin FIGS. 3C and 3D. Again, exemplary wing deflections are depicted foreach wing at three positions in a stroke. Accordingly, the vehiclegenerates roll moment to effect a left roll, according to the right handrule.

FIG. 5A depicts in a top view an aircraft 310 having a nose tip orientedin the forward direction with its left airfoil 325 deflected, e.g., 20degrees, an angle less than its right airfoil 313, e.g., 40 degrees in abackward stroke 324, 325 of the wings 312, 313. Accordingly, the leftwing 312 generates more thrust upward than the right wing 313. FIG. 5Bdepicts in a top view the aircraft 310 having a nose tip oriented in theforward direction with its left airfoil 312 deflected, e.g., 40 degrees,an angle more than its right airfoil 324, e.g., 20 degrees in a forwardstroke 314, 315 of the wings 312, 313. Accordingly, this arrangementgenerates a yaw moment counterclockwise about the vehicle 310, i.e., aleft yawing motion. FIG. 5C depicts in a top view the aircraft 310having a nose tip oriented in the forward direction with its leftairfoil 312 deflected, e.g., 40 degrees, an angle more than its rightairfoil 313, e.g., 20 degrees in a backward stroke 324, 325 of the wings312, 313. Accordingly, the right wing 313 generates more thrust upwardthan the left wing 312. FIG. 5D depicts in a top view the aircrafthaving a nose tip oriented in the forward direction with its leftairfoil 312 deflected, e.g., 20 degrees, an angle less than its rightairfoil 313, e.g., 40 degrees in a forward stroke 314, 315 of the wings312, 313. Accordingly, this generates a yaw moment about the vehicle 310in the angular direction opposite that of FIG. 5B, i.e., a right yawingmoment.

FIG. 6A depicts idealized average cumulative thrust vectors 610-611 forthe left and right sides of a vehicle, such as in FIGS. 5A and 5B, wherethe left wing fore stroke has the left wing in a high angle ofdeflection, the left wing back stroke has the left wing in a low angleof deflection, while the right wing fore stroke has the right wing in alow angle of deflection and the right wing backstroke has the right wingin a high angle of deflection. Exemplary wing deflections are depictedfor each wing at two positions in a stroke. Accordingly, in the plane ofyaw rotation 640, the horizontal components of the thrust vectors areprojected—indicating the vehicle generates yaw moment to effect acounterclockwise or left yaw maneuver. FIG. 6B depicts idealized averagecumulative thrust vectors 650-651 for the left and right sides of avehicle, such as in FIGS. 5C and 5D, where the left wing fore stroke hasthe left wing in a low angle of deflection, the left wing back strokehas the left wing in a high angle of deflection, while the right wingfore stroke has the right wing in a high angle of deflection and theright wing backstroke has the right wing in a low angle of deflection.Exemplary wing deflections are depicted for each wing at two positionsin a stroke. Accordingly, in the plane of yaw rotation 640, thehorizontal components of the thrust vectors are projected—indicating thevehicle generates yaw moment to effect a clockwise or right yawmaneuver.

Pitching moment can be generated by changing the mass balance of thevehicle, differential throttling of the flapping motor or flappingmotors, and/or cyclically changing the angles of deflections of theairfoils, i.e., cyclic pitch control. FIG. 7A depicts in a top view anaircraft 310 having a nose tip oriented in the forward direction withits left airfoil 312 and its right airfoil 312 both deflected less inthe beginning of a forward stroke (fore stroke) of the wings than thedeflection at the end of the forward stroke which is depicted as largerin deflected angle, i.e., a larger sweep angle of deflection. Thedeflection grows larger as the wing sweeps forward. Accordingly, thewings each generate more thrust upward during the beginning of theforward stroke than at the end of the forward stroke. FIG. 7B depicts ina top view an aircraft 310 having a nose tip oriented in the forwarddirection with its left airfoil 312 and its right airfoil 313 bothdeflected more in the beginning of a backward stroke (backstroke) of thewings than the deflection at the end of the backward stroke which isdepicted as smaller in deflected angle, i.e., a smaller sweep angle ofdeflection. The deflection grows smaller as the wing sweeps backward.Accordingly, the wings each generate more thrust upward during thebeginning of the backward stroke than at the end of the backward stroke.Accordingly, this cyclic pitch control generates a forward pitchingmoment, i.e., a pitching control authority about the vehicle in anangular direction that is nose downward. FIG. 7C depicts in a top viewan aircraft 310 having a nose tip oriented in the forward direction withits left airfoil 312 and its right airfoil 313 both deflected more inthe beginning of a forward stroke (fore stroke) of the wings than thedeflection at the end of the forward stroke—which is depicted as smallerin deflected angle, i.e., a smaller sweep angle of deflection. Thedeflection grows smaller as the wing sweeps forward. Accordingly, thewings each generate less thrust upward during the beginning of theforward stroke than at the end of the forward stroke. FIG. 7D depicts ina top view an aircraft 310 having a nose tip oriented in the forwarddirection with its left airfoil 312 and its right airfoil 313 bothdeflected less in the beginning of a backward stroke (backstroke) of thewings than the deflection at the end of the backward stroke which isdepicted as larger in deflected angle, i.e., a larger sweep angle ofdeflection. The deflection grows larger as the wing sweeps backward.Accordingly, the wings each generate less thrust upward during thebeginning of the backward stroke than at the end of the backward stroke.Accordingly, this cyclic pitch control generates a backward pitchingmoment, i.e., a pitching control authority about the vehicle in anangular direction that is nose upward.

FIGS. 8A and 8B depict idealized instantaneous thrust vectors 810-811,830-831 for the left and right sides of a vehicle such as in FIGS. 7Aand 7B respectively, and an idealized average cumulative thrust vector820, 840 for the vehicle such as in FIGS. 7A and 7B respectively.Exemplary wing deflections are depicted for each wing at four positionsin a stroke. Accordingly, the vehicle generates pitch moment to effect aforward (nose down) maneuver. FIGS. 8C and 8D depict idealizedinstantaneous thrust vectors 850-851, 870-871 for the left and rightsides of a vehicle such as in FIGS. 7C and 7D respectively, and anidealized average cumulative thrust vector 860, 880 for the vehicle suchas in FIGS. 7C and 7D respectively. Exemplary wing deflections aredepicted for each wing at four positions in a stroke. Accordingly, thevehicle generates pitch moment to effect a backward (nose up) maneuver.

FIG. 9 depicts an exemplary flapping drive assembly 900 including amotor 910, a gearing assembly 920, a left arm 924 and a right arm 926rotatably attached at a pin 928 of a drive gear 930, where the pin isoffset from the center of rotation of the drive gear 930. When the drivegear is rotated 931, the exemplary left rocker arm 924 and right rockerarm 926 are cyclically pushed and pulled, and thereby cause the leftmast receiver 934 and the right mast receiver 932 to swing forward andbackward.

FIG. 10A depicts, for a flapping drive assembly, the disposition of afirst capstan 1012 relative to the center of rotation of a rotatingelement 1010 that may be a gear. The second capstan (not shown in thisview) is interposed between the first capstan 1012 and the rotatingelement 1010, and both the first capstan 1012 and second capstan aremounted about a shaft 1001 that is offset from the center of rotation1002 of a rotating element 1010. FIG. 10B depicts an exemplary flappingdrive assembly and mechanism 1000 comprising: (a) a rotating element1010 having a center of rotation and a plane of rotation; (b) a firstcapstan 1012 mounted about a shaft (not shown), the shaft attached tothe rotating element 1010 distal from the center of rotation andsubstantially perpendicular to the plane of rotation; (c) a secondcapstan 1018 mounted about the shaft; (d) a first arm 1032 mounted to athird capstan 1022, a first linking member 1020 connecting the thirdcapstan 1022 with the first capstan 1012; (e) a second arm 1030 mountedto a fourth capstan 1024, a second linking member 1017 connecting thefourth capstan 1024 with the first capstan 1012; and (f) a third linkingmember 1023 connecting the third capstan 1022 with the fourth capstan1024. In some embodiments of the mechanism, the third capstan 1022 ofthe mechanism may have a center of rotation, the fourth capstan 1024 mayhave a center of rotation, and the center of rotation of the rotatingelement 1010 may be substantially collinear with both the center ofrotation of the third capstan 1022 and the center of rotation of thefourth capstan 1024. In some embodiments of the mechanism, the firstlinking member 1020 may comprise a cord, the second linking member 1017may comprise a cord, and the third linking member 1023 may comprise acord. A left wing assembly 1028 is depicted engaging the first arm 1032and a right wing assembly 1026 is depicted as engaging the second arm1030. Accordingly, a motor drives 1050 the offset capstans to effectflapping of the two wing assemblies.

FIG. 11A depicts in exploded view an exemplary wing 1100 having twocurved battens 1111, 1112, where a mast element 1120 is inserted into aleading edge sleeve 1121 of a wing airfoil membrane 1101. The sleeve1121 may be formed by drawing the airfoil membrane back on itself and/ormay include a tube for receiving the mast element—a tube about which theairfoil may be wrapped and fixed. Resilient washers 1122, 1123 may bedeposed at the proximal and distal portions of the mast element 1120 oneach side of the leading edge sleeve 1121. A root spar element 1130, orboom element, is inserted into the root spar sleeve 1131 of the wingairfoil membrane 1101. The boom sleeve 1131 may be formed by drawing theairfoil back on itself and/or may include a tube for receiving the mastelement—a tube about which the airfoil may be wrapped and fixed.Resilient washers 1132, 1133 may be deposed at the proximal and distalportions of the root spar element 1130 on each side of the boom sleeve1131. The mast element 1120 and boom element 1130 engage a cornerelement 1140, or arm fitment, that is configured to be received by anarm socket element (not shown). FIG. 11B depicts an assembled exemplarywing 1100. The membrane may be made of extruded polyethylene foam sheet,e.g., having 1/32 inch thickness such as packing foam sheets. Thebattens 1111, 1112, mast element 1120, boom element 1130, and sleevetubes 1121, 1131 may be made of carbon filaments. The wing 1100 mayfurther include a pocket made from overlapping the membrane proximate tothe root spar, or boom, and interposing between the layers of membrane alayer of foam fabric. The foam fabric may damp vibrations and reduceacoustical effects of flapping.

FIG. 12 depicts an exemplary flapping drive assembly and mechanism 1200comprising a left flapping drive assembly 1210 and a right flappingdrive assembly 1220, similar to combining a pair of the embodiments ofFIG. 10B, where each right and left flapping drive assemblies has fourcapstans, but one arm for a wing assembly. The embodiment of FIG. 12depicts a left wing assembly 1230 engaging the arm of a left portion1211 of the flapping drive assembly 1200, where the arm 1211 of the leftassembly 1210 engages the third capstan 1212 of the left assembly 1210.The embodiment of FIG. 12 also depicts a right wing assembly 1240engaging the arm 1213 of the right assembly 1220, where the arm 1213 ofthe right assembly 1220 engages the fourth capstan 1212 of the rightassembly 1220. In this exemplary embodiment, a processor such as acentral processing unit (CPU), having load instructions, maintainssynchronization between the left and right motor by monitoring inputsfrom wing position sensors 1240, 1241. Pitch control authority may begenerated by differential front and rear engine throttling. Yaw controlauthority may be generated by differential forestroke and rearstrokethrottling, and roll control authority may be generated by differentialmidstroke and endstroke throttling, and done so with a wing-mountedspring, e.g., a luffing spring attached to the root spar, or boom.Accordingly, servos to adjust the angles of deflection of the wings arenot required for this exemplary embodiment.

FIG. 13 depicts an exemplary assembly for limiting root spar, or boom,travel 1300. Two servos 1310, 1320 are used, each controlling by astring, or a cord, fed via eyelets 1370-1379, and a pulley system 1330the position of boom stops, 1360-1363, to allow for differentialdeflection of each airfoil (not shown). Each boom stop is affixed to arocker-like pulley element that may be in tension, and the drawing backon the string opens the angle between opposing boom stops. A pair ofboom stops are disposed on each of the arms of the flapping assembly sothat the boom stops rotate with the flapping arm to limit the travel ofthe proximal end of the boom. Accordingly, roll and yaw authority may begenerated during mast flapping by the positioning of the boom stops.Aerodynamic forces tend to cause the boom to stop on the trailing boomstop of the stroke, i.e., the aftward boom stop during a forward strokeand the forward boom stop during a backward stroke. A handlebar-likestructure 1380 may be added that may be rotated 1382, via a pitch servo1381, to extend or retract, in conjunction with the mast flappingmotion, the boom stops on each wing. The handlebar-like structure 1340,1350 may be used to generate pitch authority during flapping bycontinually repositioning the boom stops during strokes. FIG. 14Adepicts in a side view the exemplary assembly 1400 of FIG. 13 where thepair of strings or cords 1410, 1412 are shown threaded though an eyelet1414 at end of an arm of the handlebar-like structure 1416. The servoshown may be disposed proximate to the flapping motor and the flappingdrive assembly. A boom stop 1363 may be mounted on a pulley element thatitself is mounted in tension to a support structure. FIG. 14B depicts arotation 1430 of the handlebar element 1416 by the pitch servo 1318causing the strings to allow the boom stops 1363, 1362 to retract, for aparticular portion of the stroke. That is, the stings would draw on theboom stop pulleys as the mast rotates (out of the page in thisillustration). FIG. 13B depicts a rotation 1431 of the handle barelement by the pitch servo 1318 causing the strings to draw on the boomstops 1362, 1363 to extend the angle between each for a particularportion of the stroke.

In a view orthogonal to the plane of a mast and root spar, or boom, FIG.15A depicts the motion of a string 1510 to rotate the position of afirst boom stop 1520 by rotating a first pulley element (obstructed inthis view by a second pulley element 1530) about a pivot point on asupport structure. Also depicted in FIG. 15A is a second string 1511that does not move in this example, leaving the second boom stop 1521 ina stationary position—at this position in a stroke—as the tension in thestring balances the tension in the mounted second pulley element 1530.FIG. 15B depicts in a bottom up view of FIG. 13 where the boom stops1360-1363 are extended to a relatively high deflecting angle of theboom. FIG. 15B depicts the bottom up view of FIG. 13 where the flappingmotion of the arms has caused the wings to change relative angles in thestroke, and that the boom stop 1360-1363 remain extended as the sameangle as in FIG. 15B. That is, the pitch actuator may be at a neutralposition so as to not affect the deflection angle during a stroke of theexemplary embodiment of FIG. 14A.

FIG. 16 depicts a wing assembly 1600 and the pair of pulley elements forthe boom stops 1614, 1616. With the application of the two strings, eachthat may be under the control of a bi-directional servo (not shown),each pulley element may be placed in tension and each boom stop may beangularly positioned independent of the other. FIG. 17A depicts anexample where each boom stop 1710, 1720 is positioned to allow arelatively large deflection angle for both the forward stroke and thebackward stroke. With the stops opened wide, a flapping wing such asthis has a relatively low angle of attack and generates relatively lowthrust. In contrast, FIG. 17B depicts an example where each boom stop1711, 17

+21 is positioned to allow a relatively small deflection angle for boththe forward stroke and the backward stroke. With the stops open to anarrow position, a flapping wing such as this has a relatively highangle of attack and generates relatively high thrust with anaccompanying relatively larger magnitude of downwash. FIGS. 18A-18Cdepict yaw control 1800 effected by modulating the boom stops left orright to generate a net yawing moment. FIG. 18A depicts stops 1810, 1812in a neutral position as to the yaw channel. That is, a flapping armwould have the same boom angle of deflects in the forward stroke as inthe backward stroke, i.e., the thrust vector would be aligned with the“upward” direction of the aircraft. FIG. 18B depicts stops 1814, 1816biased to the right where the flapping of the wing and movement of theboom between the two stops—to one stop during the forward stroke and tothe other stop during the rearward stroke—would generate a thrust vectorhaving a right-oriented component. Accordingly, during flapping, thevehicle effecting stops biased to the right would execute a nose leftcommand. FIG. 18C depicts stops 1818, 1820 biased to the left where theflapping of the wing and movement of the boom between the two stops—toone stop during the forward stroke and to the other stop during therearward stroke—would generate a thrust vector having a left-orientedcomponent. Accordingly, during flapping, the vehicle effecting stopsbiased to the left would execute a nose right command.

FIG. 19 depicts an alternate means of boom travel control 1900 where acord or string is controlled by a servo (not shown) and fed, via eyelets1911, 1912 on a yoke 1910, to the boom 1920, and fixed at a distalportion of the boom. FIGS. 20A and 20B depicts control of theorientation of the boom 2024 during flapping 2010, 2020, and theorientation of the boom 2024 may be effected by rotating the cord 2030or string to position the boom for a backward stoke, as in FIG. 20A, andby rotating the cord 2022 or string to position the boom 2024 for abackward stroke. The positioned deflection angle may be effected duringa stroke and thus may effect control authority for pitch (e.g., viacyclic modulation), yaw, and roll based on a continually changing servoposition commands.

A structural element termed a yang may be attached to the wing-boomstructure via a ball joint a multiple axis joint and may disposegenerally parallel to the boom. The boom or the yang may engage a yokeand the luffing of the membrane can be affected by the motions of theyoke. FIG. 21A depicts a three-axis servo boom and/or yang assembly 2100as another means of boom travel control where a boom (or yang)restraining yoke 2110 may increase or reduce luffing, i.e., the affectsof the wing membrane slack, for both wings during a stroke to generatepitch control authority via a first servo and gearing assembly 2120;effect a differential amount of luff between the wings during a stroketo generate roll control authority via a second servo and gearingassembly 2130; and optionally effect a bias in boom travel via a thirdservo and gearing assembly 2140 to generate a luff differential for yawcontrol. Accordingly, the assembly 2100 provides multiple axes oforientation for the yoke to the body of the aircraft to adjust wingmembrane luff during strokes to effect three axes of control.

FIG. 21B depicts an exemplary aircraft having a flapping mechanism 2100as described in FIG. 10B (1000), and the root spar, or boom, controlmechanism as described in FIG. 21A (2100). In the embodiment of FIG.21B, the boom 2161 of each wing 2160 engage the yoke 2110. Also depictedabove the flapping mechanism are a power and processing module 2170. Thevehicle may include an optional stand 2180. FIG. 22 depicts a portion ofan exemplary aircraft 2200 having a flapping mechanism as described inFIG. 9 (900), and the root spar, or boom, control mechanism as describedin FIG. 21A, where the root spars 2161, 2262 engage the yoke 2110. TheFIG. 23 depict a portion of an exemplary aircraft 2300 having a flappingmechanism as described in FIG. 9 (900), and another embodiment of theroot spar, or boom, control mechanism as described in FIG. 21A (2100),where the root spars 2161, 2262 engage the yoke 2110. FIG. 24A depictsthe positionable yoke 2110 tilted toward the left airfoil 2410 and awayfrom the right airfoil 2420. The masts of each wing remain in theflapping plane and so the luffing, or wing slack effect, of the leftairfoil 2410 enhances as the membrane is looser than the right airfoil2420, and accordingly the left airfoil 2410 generates less thrust thanthe right airfoil 2420. FIG. 24B depicts the gimbaled yoke tilted towardthe right airfoil 2410 and away from the right airfoil 2420. The mastsof each wing remain in the flapping plane and so the luffing of theright airfoil is more than the luffing of the left airfoil 2420, andaccordingly the right airfoil 2420 generates less thrust than the leftairfoil 2410. FIGS. 24A and 24B illustrate a roll control authority forthis exemplary embodiment. The control gimbal having a yoke may directlymove the trailing edge ends of the root spars to manipulate the luff inthe wing.

FIG. 25A depicts a boom yang system 2500 where separate boom yang 2510engages the yoke 2110 and provides structural support 2511 for avariable boom stop lever 2512. Decoupling yaw control from the pitch androll control provided by the multiple axis yoke positing assembly may beaccomplished by allowing the root spar 2520 to move freely betweenadjustable boom stops 2521, 2522, and having a yang 2510 or otherstructural element connect the movement of the yoke arms 2111, 2112 ofthe yoke 2110 with the orientation of the wing at a multiple-axis joint2550. Accordingly, the roll control may be effected by the side tiltposition of the yoke of a two-axis gimbal of servo assembly—similar tothe assembly of FIG. 21A but without the yaw servo gear box, and thepitch control may be effected by the fore and aft tilt position of theyoke. A third (yaw) servo is used to control the orientation of the boomstops 2521, 2522 attached to a lever 2512 by pulling or releasing alever, e.g., via a cable 2513. FIG. 25B depicts an embodiment of thelever 2512, that may be mounted to the yang structure 2511 in tension,and actuated via a cable 2513 attached to the boom yang structure 2511.FIG. 25C depicts the cable 2513 pulling the lever 2512 to shorten theboom 2590 travel distance of the boom stops. FIG. 25D depicts the cable2513 releasing the lever 2512 to allow the travel distance of the boom2590 to lengthen.

FIG. 26 is an exemplary top level block diagram of the control andpropulsion system of an aircraft embodiment 2600. A central processingunit (CPU) 2602, having addressable memory and drawing from an onboardpower supply 2608 comprising a battery, generates voltage commands to atleast one drive motor, i.e., a thrust or flapping, motor 2610. Thecommands may be pulse width modulated (PWM). A Hall sensor may bedisposed at the crankshaft so that flapping frequency may be derived andprovided to the CPU 2602. In some embodiments there are three controlservos 2612, 2614, 2616 and so, FIG. 26 depicts the CPU 2602 generatingcommands to a pitch bi-directional servo 2612, a roll bi-directionalservo 2614, and a yaw bi-directional servo 2616. Position sensors 2624,2626, 2628 can feed back to the CPU 2602 each servo position 2610, 2612,2614, 2616. Angular rate measuring devices such as two, two-axisgyroscopes 2618, 2620 may be used to provide yaw angular rate, pitchangular rate, and roll angular rate. The CPU 2602 may provide externalcommand signals from a radio controller 2622 by an uplink and the CPU2602 may provide status or other information via a downlink. Generally,the CPU 2602 may communicate with an external node via a transceiver.Electrical and/or electronic elements may be powered via an onboardpower supply and or local chemical battery elements 2608.

FIG. 27 is a top level functional block diagram 2700 of a flappingfrequency controller where the command flapping frequency, F_(C), 2702and the derived flapping frequency F_(est) 2704 are differenced togenerate a flapping frequency error, ε 2706. The flapping frequencyerror 2706 is integrated and multiplied by a gain, K_(I), 2708 and theflapping frequency error 2706 is multiplied by a gain, K_(P) 2710. Thesetwo products are combined, along with the product of the flappingfrequency multiplied by a gain, K_(FF), 2712 to generate a command,e.g., a main motor voltage command, to the drive or thrust motor forflapping. The flapping frequency controller, along with gains or stepsto generate gains, may be expressed in machine-readable language, storedin memory accessible by the aircraft processor, and executed to generatethe flapping motor voltage commands.

FIG. 28 is an exemplary top level block diagram of a servo controller2800 where a position command, d_(c), 2802 is differenced from themeasured position, d_(MEAS), 2804 to generate a servo position error,d_(ε), 2806 and then the servo position error is multiplied by a servogain K_(δ), 2808 to generate servo motor voltage command, u 2810. Perservo channel, the servo controller 2800, along with gains or steps togenerate gains, may be expressed in machine-readable language, stored inmemory accessible by the aircraft processor, and executed to servo motorvoltage commands for one or more servos.

FIG. 29 is an exemplary top level block diagram of an angular ratecontroller 2900 that may be implemented for roll, pitch, or yaw ratecontrol. A biased angular rate 2902 measurement may be generated bydifferencing the filtered gyro rate 2904 measurement and a gyro ratebias based on one or more gyro readings stored at throttle-up, i.e.,before the wings start flapping. An angular error rate, e, 2906 may begenerated by differencing the angular rate command and the biasedangular rate 2902 measurement. The servo position command, δ_(C), 2908may be generated by combining the product of the angular rate commandand a feed forward gain, K_(FF), 2910 with the product of the angularerror rate 2906 and a proportional rate gain, K_(P) 2912.

FIG. 30 is an exemplary top level block diagram of an angular ratecontroller 3000 that may be implemented for roll, pitch, or yaw ratecontrol. A biased angular rate measurement 3002 may be generated bydifferencing the filtered gyro rate measurement 3004 and a gyro ratebias based on one or more gyro readings stored at throttle-up, i.e.,before the wings start flapping. A digital integrator may integrate overtime the angular error rate, e, 3006. An angular error rate, e, 3006 maybe generated by differencing the angular rate command and the biasedangular rate measurement. The servo position command, δ_(C), 3008 may begenerated by combining the product of the angular rate command and afeed forward gain, K_(FF), 3010 with the product of the angular errorrate and a proportional rate gain, K_(P), 3012 and along with theproduct of the integrated angular error rate multiplied by a gain, K_(I)3014.

FIG. 31 depicts an exemplary wing having mast, root spar and a membranehaving a mast fold-over portion 3100 and a root spar fold-over portion3120, and first batten 3130. FIG. 32 depicts in cross sectional view thewing of FIG. 31 where a first batten 3130 is a rod-shaped filamentdisposed on the membrane surface, the second batten 3140 isparallelepiped-shaped. FIG. 33 depicts in an edge on view of FIG. 31depicting rotatability of the membrane about the mast. FIG. 34 depictsin a cross section view of wing FIG. 31 where the membrane 3103 wrappedaround a 3400 tube within which is disposed the mast, or root-to-wingtipspar. The overlapping surfaces of the membrane may be joined in part byan epoxy or heat treatment. FIG. 35 depicts another means of attachmentwhere a separate piece of material 3500, that may be the same materialas the membrane, is used to attach the tube 3400 to the membrane 3103.FIG. 36 depicts another means of attachment where the membrane edge 3610has a t-shape portion 3611 when viewed edge on, and the t-shapedportion, or orthogonal edge surface, is inserted within the mast tube3620 along a slit, and may be held in place by pressure of the mastelement of fixed via heat or epoxy. FIG. 37 depicts an exemplary airfoilhaving two battens a membrane fold-over portions. FIG. 38 depicts anexemplary airfoil having two battens and membrane fold-over portions,where the battens have membrane overlays, 3810, 3811. FIG. 39 depictsthe airfoil of FIG. 37 having two battens 3710, 3711 and two fold-overregions 3720, 3721, and where the membrane material is a foam membrane.FIG. 40 depicts an airfoil without battens and no membrane fold-overs.FIG. 41 depicts an airfoil having two battens, membrane fold-overs andan arcuate cutout region 4100 between the mast 4110 and the root spar4120. FIG. 42 depicts an angular airfoil planform of reduced surfacearea when compared with other examples, and without fold-over regions orbattens. FIG. 43 depicts an airfoil made of a foam membrane having twocurving battens 4310, 4311, and membrane fold-overs. FIG. 44 depicts afixture 4400 for making an airfoil with the mast 4410 and root spar 4420attached to the fixture 440, and the tubes 4430 and 4440 available. FIG.45 depicts a membrane blank 4500 having a filament grid fixed to aworking surface. FIG. 46 depicts the fixture of FIG. 44 positioned overthe membrane blank. FIG. 47 depicts a cutting of the membrane andfold-over step along the mast and root spar. FIG. 48 depicts the battens5011, 5012 applied to the surface of the membrane and a cut step for theremainder of the planform. FIG. 49 depicts a removal of an exemplaryairfoil 5110 from the blank 4500.

One of ordinary skill in the art will appreciate that the elements,components, steps, and functions described herein may be furthersubdivided, combined, and/or varied, and yet, still remain within thespirit of the embodiments of the invention. Accordingly, it should beunderstood that various features and aspects of the disclosedembodiments may be combined with, or substituted for one another inorder to form varying modes of the invention, as disclosed by example.It is intended that the scope of the present invention herein disclosedby examples should not be limited by the particular disclosedembodiments described above. Accordingly, the invention has beendisclosed by way of example and not limitation, and reference should bemade to the following claims to determine the scope of the presentinvention.

1. An air vehicle comprising: a support structure comprising: a flappingdrive element; a first airfoil rotatably attached to the supportstructure; and a second airfoil rotatably attached to the supportstructure; wherein the first airfoil comprises a first root spar and afirst membrane attached to the first root spar, the first airfoilconfigured to be driven to flap via the flapping drive element; andwherein the second air foil comprises a second root spar and a secondmembrane attached to the second root spar, the second airfoil configuredto be driven to flap via the flapping drive element; wherein air vehiclecontrol about at least one axis of the vehicle is effected by at leastone of: a variable membrane luffing; variable root spar rotation travellimitation; and variable flapping angular velocity of the flapping driveelement; and wherein the flapping drive element comprises: a rotatingelement having a center of rotation and a plane of rotation; a firstcapstan mounted about a shaft, the shaft attached to the rotatingelement distal from the center of rotation and substantiallyperpendicular to the plane of rotation; a first rocker member rotatablyattached to a support structure; a first drive link rotatably attachedto the first capstan and the first rocker member; a first arm rotatablyattached to the support structure and rotatably attached to the firstrocker member via a first rocker link; a second capstan mounted aboutthe shaft; a second rocker member rotatably attached to the supportstructure; a second drive link rotatably attached to the second capstanand the second rocker member; and a second arm rotatably attached to thesupport structure and rotatably attached to the second rocker member viaa second rocker link.
 2. The air vehicle of claim 1 wherein the rotatingelement is rotatably attached to the support structure.
 3. An airvehicle comprising: a support structure comprising: a flapping driveelement; a first airfoil rotatably attached to the support structure;and a second airfoil rotatably attached to the support structure;wherein the first airfoil comprises a first root spar and a firstmembrane attached to the first root spar, the first airfoil configuredto be driven to flap via the flapping drive element; and wherein thesecond air foil comprises a second root spar and a second membraneattached to the second root spar, the second airfoil configured to bedriven to flap via the flapping drive element; wherein air vehiclecontrol about at least one axis of the vehicle is effected by at leastone of: a variable membrane luffing; variable root spar rotation travellimitation; and variable flapping angular velocity of the flapping driveelement; and wherein the flapping drive element comprises: a rotatingelement having a center of rotation and a plane of rotation; a firstcapstan mounted about a shaft, the shaft attached to the rotatingelement distal from the center of rotation and substantiallyperpendicular to the plane of rotation; a second capstan mounted aboutthe shaft; a first arm mounted to a third capstan, a first linkingmember connecting the third capstan with the first capstan; a second armmounted to a fourth capstan, a second linking member connecting thefourth capstan with the second capstan; and a third linking memberconnecting the third capstan with the fourth capstan.
 4. The air vehicleof claim 3 wherein the third capstan has a center of rotation, thefourth capstan has a center of rotation, and the center of rotation ofthe rotating element is collinear with the center of rotation of thethird capstan and the center of rotation of the fourth capstan.
 5. Theair vehicle of claim 4 wherein the first linking member comprises acord, the second linking member comprises a cord, and the third linkingmember comprises a cord.
 6. An air vehicle comprising: a supportstructure comprising: a flapping drive element; a first airfoilrotatably attached to the support structure; and a second airfoilrotatably attached to the support structure; wherein the first airfoilcomprises a first root spar and a first membrane attached to the firstroot spar, the first airfoil configured to be driven to flap via theflapping drive element; and wherein the second air foil comprises asecond root spar and a second membrane attached to the second root spar,the second airfoil configured to be driven to flap via the flappingdrive element; wherein air vehicle control about at least one axis ofthe vehicle is effected by at least one of: a variable membrane luffing;variable root spar rotation travel limitation; and variable flappingangular velocity of the flapping drive element; and wherein the flappingdrive element comprises: a first motor driving a first rotating element,the first rotating element having a center of rotation and a plane ofrotation; a first capstan mounted about a shaft, the shaft attached tothe rotating element distal from the center of rotation andsubstantially perpendicular to the plane of rotation; a second capstanmounted about the shaft; a first arm mounted to a third capstan, a firstlinking member connecting the third capstan with the first capstan; asecond linking member connecting the fourth capstan with the secondcapstan; and a third linking member connecting the third capstan withthe fourth capstan; a second motor driving a second rotating element,the second rotating element having a center of rotation and a plane ofrotation; a fifth capstan mounted about a second shaft, the second shaftattached to the second rotating element distal from the center ofrotation and substantially perpendicular to the plane of rotation of thesecond rotating element; a sixth capstan mounted about the second shaft;a fourth linking member connecting the seventh capstan with the fifthcapstan; a second arm mounted to a eighth capstan, a fifth linkingmember connecting the eighth capstan with the sixth capstan; and a sixthlinking member connecting the seventh capstan with the eighth capstan;and circuitry controlling a flapping rate of the first motor and thesecond motor.